Question

已知a+b=2 求a的3次方+6ab+b的3次方的值.

Answer 1

a^3+6ab+b^3

=(a^3+b^3)+6ab

=(a+b)(a^2+b^2-ab)+6ab

=2(a^2+b^2-ab)+6ab

=2(a^2+b^2+2ab)

=2(a+b)^2

=8